Biomedical Engineering Reference
In-Depth Information
The theory of pattern formation was originally inspired by a desire to ex-
plain tissue differentiation (54). The theory showed that in a reaction-diffusion
system chemical inhomogeneities could arise spontaneously, and that these in-
homogeneities could confer distinct attributes to different parts of a tissue. Yet,
the link between this theory and experiments remains tenuous because of the
difficulties encountered in identifying the variables of the theory, namely, the
activators and the inhibitors. In recent years, it has become evident that there are
chemical inhomogeneities even within a single cell. The chemical and morpho-
logical polarization observed in the eukaryotic gradient sensing mechanism is a
paradigm of such subcellular pattern formation. Given our deep understanding
of cellular and molecular biology, it would not be surprising if pattern formation
theory faces its first rigorous experimental tests at the level of cells rather than
tissues.
4.
ACKNOWLEDGMENTS
We would like to thank Professor D.A. Lauffenburger (MIT) for introduc-
ing us to the problem and for highlighting the important questions. We are also
grateful to Dr. Orion Weiner (Harvard) and Professor Richard Dickinson (Uni-
versity of Florida) for their thoughtful comments.
5.
NOTES
1. Abbreviations used: PI = phosphatidylinositol; PIP = phosphatidylinosi-
tol 4-phosphate; PIP
2
= phosphatidylinositol 4,5-phosphate; PIP
3
= phosphatidy-
linositol 3,4,5-phosphate; DG = diacylglycerol; IP
3
= inositol 1,4,5-triphosphate;
PI3K = phosphatidylinositol 3-kinase; PI5K = phosphatidylinositol 4-phosphate
5-kinase; PITP = phosphatidylinositol transport protein.
2. To be sure, this implies that the angular gradients are also negligibly
small, and this will be borne out by the simulations below. We retain the angular
variation only because it simplifies the numerical simulations. Neglecting the
angular variation yields an inconvenient "mixed" system of equations containing
an ODE describing the evolution of the inositol phosphates along with the other
PDEs. At any rate, we suffer no loss of generality by retaining the angular varia-
tion.
6.
REFERENCES
1.
Martin P. 1997. Wound healing—aiming for perfect skin regeneration.
Science
,
276
:75-81.
2.
Jones G. 2000. Cellular signaling macrophage migration and chemotaxis.
J Leuk Biol
68
:593-
602.
